Problem: Rachel earned $\$34$ in $4$ hours at her job today. She wants to know how much she could earn $(e)$ tomorrow if she works $10$ hours at the same hourly rate. How much will Rachel earn in $10$ hours? $\$$
We're dealing with a proportional relationship, so each ratio of earnings to hours must be equivalent. Here's one way to write the proportion: $\dfrac{\$34}{4\text{ hours}} = \dfrac{\$e}{10\text{ hours}}$ Now, solve the proportion for $e$ : $\begin{aligned} \dfrac{34}{4} &= \dfrac{e}{10} \\\\ \dfrac{17}{2} &= \dfrac{e}{10} \\\\ \dfrac{e}{10} &= \dfrac{17}{2} \\\\ e &= \dfrac{17}{2} \cdot 10 \\\\ e &= \dfrac{17\cdot 10}{2} \\\\ e &= \dfrac{17\cdot \stackrel{5}{\cancel{10}} }{\underset{1}{\cancel2}} \\\\ e &= \dfrac{17 \cdot 5}{1} \\\\ e &= \dfrac{85}{1} \\\\ e &= 85 \end{aligned}$ Rachel will earn $\$85$ in $10$ hours.